A007069 First column of spectral array W(sqrt 2). (Formerly M1329)

1, 2, 5, 7, 9, 11, 12, 15, 16, 19, 21, 22, 25, 26, 29, 31, 33, 35, 36, 39, 41, 43, 45, 46, 49, 50, 53, 55, 57, 59, 60, 63, 65, 67, 69, 70, 73, 74, 77, 79, 80, 83, 84, 87, 89, 91, 93, 94, 97, 98, 101, 103, 104, 107, 108, 111, 113, 115, 117, 118, 121, 123, 125, 127, 128, 131

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.

Formula

From Benoit Cloitre, Apr 06 2003: (Start)

Iterated floor function: a(n) = floor(sqrt(2)*floor(sqrt(2)*n)).

a(n) = A001951(A001951(n)).

a(n) = 2*n - 1 - A059648(n). (End)

Mathematica

Table[Floor[Sqrt[2]*Floor[Sqrt[2]*n]], {n, 1, 100}] (* G. C. Greubel, Aug 16 2018 *)

Prog

(PARI) vector(100, n, floor(sqrt(2)*floor(n*sqrt(2)))) \\ G. C. Greubel, Aug 16 2018
(Magma) [Floor(Sqrt(2)*Floor(Sqrt(2)*n)): n in [1..100]]; // G. C. Greubel, Aug 16 2018
(Python)
from math import isqrt
def A007069(n): return isqrt(isqrt(n**2<<1)**2<<1) # Chai Wah Wu, Aug 29 2022

Crossrefs

Cf. A001951, A059648.

Sequence in context: A007300 A256699 A247421 * A182463 A163985 A130773

Adjacent sequences: A007066 A007067 A007068 * A007070 A007071 A007072

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from Benoit Cloitre, Apr 06 2003

Status

approved